Question

X-2/x+3 - 30/x^2-9 - 3 = 0

Answer 1

а² - b² = (a - b)(a + b) - разность квадратов

(х-2)/(х+3) - 30/(х²-3²) - 3 = 0

(х-2)/(х+3) - 30/(х-3)(х+3) - 3/1 = 0

Приводим дроби к общему знаменателю (х-3)(х+3)

(х - 2) · (х - 3) - 30 - 3 · (х² - 3²) = 0

х² - 2х - 3х + 6 - 30 - 3х² + 27 = 0

(х² - 3х²) - (2х + 3х) + (6 - 30 + 27) = 0

-2х² - 5х + 3 = 0    | умножим обе части уравнения на (-1)

2х² + 5х - 3 = 0

D = b² - 4ac = 5² - 4 · 2 · (-3) = 25 + 24 = 49

√D = √49 = 7

х = (-b±√D)/(2а)

х₁ = (-5-7)/(2·1) = (-12)/2 = -6

х₂ = (-5+7)/(2·1) = 2/2 = 1

Ответ: (-6; 1).

Answer 2

Надеюсь помогла
удачи тебе.............

Answer 3

To solve the equation $\frac{X-2}{X+3} - \frac{30}{X^2-9} - 3 = 0$, you'll want to first simplify the equation by finding a common denominator and combining the fractions.

The common denominator for the fractions is $X^2 - 9$, which can be factored as $(X+3)(X-3)$. So, rewrite the fractions with the common denominator:

$\frac{(X-2)(X-3)}{(X+3)(X-3)} - \frac{30}{(X+3)(X-3)} - 3 = 0$

Now that the fractions have a common denominator, you can combine them into a single fraction:

$\frac{(X-2)(X-3) - 30 - 3(X+3)(X-3)}{(X+3)(X-3)} = 0$

Next, expand and simplify the numerator:

$X^2 - 5X + 6 - 30 - 3(X^2 - 9) = 0$

Now, distribute the -3 on the right side:

$X^2 - 5X + 6 - 30 - 3X^2 + 27 = 0$

Combine like terms:

$-2X^2 - 5X - 24 = 0$

Now, you have a quadratic equation. To solve for X, you can use the quadratic formula:

$X = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this case, $a = -2$, $b = -5$, and $c = -24$. Plugging these values into the formula:

$X = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(-2)(-24)}}{2(-2)}$

Simplify further:

$X = \frac{5 \pm \sqrt{25 - 192}}{-4}$

Since the discriminant (the value inside the square root) is negative, this equation has no real solutions. The solutions are complex numbers. If you want to find the complex solutions, you can continue the calculation, but they won't be real numbers.